Question: A circle has a radius of $10$. An arc in this circle has a central angle of $84^\circ$. What is the length of the arc? ${20\pi}$ ${84^\circ}$ $\color{#DF0030}{\dfrac{14}{3}\pi}$ ${10}$
Answer: First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (10) = 20\pi$ The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{84^\circ}{360^\circ} = \dfrac{s}{20\pi}$ $\dfrac{7}{30} = \dfrac{s}{20\pi}$ $\dfrac{7}{30} \times 20\pi = s$ $\dfrac{14}{3}\pi = s$